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Statistics 2 Shira Farby Parametric statistics Reading: Field, A. & G. Hole. 2003. How to design and Report Experiments. London: A Sage Publications Company, 120-139; 141-155 Last time: we looked at models for central tendency (mean, median, mode) Today: we look at how much the data is spread / varied. Key terms: Deviation, sun of squared errors, variance, standard deviation Term mean Deviation sun of squared errors variance formula Definition in words ∑𝑥 𝑁 𝐷𝑒𝑣 = 𝑥 − 𝑥 𝑥̅ = 𝑆𝑆 = ∑(𝑥 − 𝑥)2 𝑆𝑆 𝑁−1 𝑆𝐷 = √𝑆 2 𝑆2 = standard deviation 𝑆𝐷 = √ Degrees of freedom Standard error ∑(𝑥 − 𝑥)2 𝑁−1 𝑑𝑓 = 𝑁 − 1 𝑆𝐸 = 𝑆𝐷 √𝑁 Sample-population Key terms: sampling distribution of the mean, standard error, source of variance, confidence interval sampling distribution of the mean standard error source of variance confidence interval Statistics 2 Shira Farby Class practice An experiment compared children with specific language impairment (SLI) and children who are typically developing (TD). The research hypothesis was that the groups will have different responses to different word order. 30 Children were tested, each was presented with 10 sentences (5 SVO, 5 VSO). The task was sentence repetition, and the response measure was whether the verb was produced correctly (yes/no) Before we begin: Which are the independent variables in this design? Which are the dependent variables? On what scale? How many conditions? Within subject or between subject? Describe the findings: In a _____ design of _____ conditions, the effect of ___________________________ as the independent variable(s) on _________________________as the dependent variable(s) was measured in a ___________________task. Mean responses and standard deviations are presented below: MEAN SD Statistics 2 Shira Farby Inferential statistics H0= the experiment has no effect The purpose of statistical inference is to reject this hypothesis H1 = the mean of the population affected by the experiment is different from the general population In order to reject the null hypothesis, we check if our sample belongs to the population under H1 or H0 Is the difference between the sample and the population big enough to reject H0? Key terms: level of significance, critical value, reject the null hypothesis, power of the effect Statistical tests t-tests Paired t-test Independent t-test ANOVA (Comparing Means of more than two samples) One way ANOVA Two-Way Independent ANOVA Two-Way Repeated Measures ANOVA Two-Way Mixed ANOVA